Considerable effort has gone into building numerical weather and ocean prediction models during the past 50 years. Less effort has gone into the visual representation of output from those forecast models and many of the techniques used are known to be ineffective. The effectiveness of a data display depends on how well critical patterns can be perceived. This paper outlines a set of perceptual principles for what makes a good representation of a 2D vector field and shows how these principles can be used for the portrayal of currents, winds, and waves. Examples are given from a series of evaluation studies that examine the optimal representation of these variables. The results suggest that for static graphic presentations, equally spaced streamlines may be optimal. If wind barbs are curved to follow streamlines, perception of local wind speed and direction as well as the overall pattern is improved. For animated portrayals of model output, animated streamlets can perceptually separate layers of information so that atmospheric pressure and surface temperature can clearly be shown simultaneously with surface winds.
The theory of human pattern perception is applied to the portrayal of winds, waves, and ocean currents, resulting in significant improvements in interpretation.
While a great deal of effort has gone into building numerical weather and ocean prediction models during the past 50 years, less effort has gone into the visual representation of output from those forecast models and many of the techniques used are known to be ineffective. In particular, the representation of vector fields (winds, currents, or waves) is almost always done using grid patterns of small arrows or wind barbs (Fig. 1) despite studies showing other methods to be far superior (Laidlaw et al. 2005; Pilar and Ware 2013). Other methods such as streamlines have been available for decades (e.g., Saucier 1955) but are rarely used. Yet representation is critical; ultimately, visualization is the only viable method for interpreting complex patterns of winds and currents as well as for scalar fields such as pressure and temperature. The need for improved visualization methods becomes even more significant with the continued increases in the spatial resolution and data density of numerical ocean and weather forecast models.
Most prior research into the visualization of ocean currents and winds has focused on applying new visualization techniques to the model output. Examples include methods for creating equally spaced streamlines (Turk and Banks 1996; Jobard and Lefer 1997), applying the technique of line integral convolution (Jobard et al. 2002) whereby digital noise patterns are advected in the direction of flow, and applying volume rendering methods (Max et al. 1993; Kniss et al. 2002) to 3D flow model output. Others have examined the technical problem of dealing with nested grids commonly used with flow models (Treinish 2000) or time-varying gridded data (Doleisch et al. 2005). There have also been tour de force designs such as Baker and Bushell's (1995) carefully crafted, unique representation of a storm cloud done in consultation with Edward Tufte (Tufte 1997).
In contrast, relatively little effort has gone into formal evaluation aimed at comparing different portrayal methods. An exception is Laidlaw et al.'s (2005) study of six different alternative representations of the same flow pattern. Among other things, this revealed equally spaced streamlines to be more effective than arrow grids. Another study by Martin et al. (2008) showed systematic biases in the perception of wind direction when grids of wind barbs were used to show spiral patterns around a hurricane center. These studies provide invaluable insights and are first steps in placing flow representation on a scientific footing. But their findings are difficult to generalize. There are many ways that arrows can be used to show flow, for example. The arrows can have different spacing, lengths, widths, and colors. Perhaps the result of Laidlaw et al.'s (2005) study would have been different with different kinds of arrows. The solution to this problem is to develop a theory of effective flow representation. Such a theory can guide designs, and it can be tested and refined by means of experiments with human participants. We contend that such a theory should be based primarily on the science of human perception.
The effectiveness of a data display depends on how well critical patterns can be perceived and vision science can tell us something about this. In this paper, we outline the perceptual principles for what makes a good representation of a 2D vector field and show how these principles can be used in design. We present a number of displays that we have designed according to these principles and evaluated in various ways using forecast guidance from the National Oceanic and Atmospheric Administration (NOAA) and U.S. Navy operational numerical weather and oceanographic forecast modeling systems.
PERCEPTUAL PRINCIPLES FOR REPRESENTING VECTOR FIELDS.
From the point of view of understanding what makes a flow visualization effective, the most important part of the brain is the primary visual cortex (V1). Fortunately, more than 50 years of neuroscience research has investigated the operation and function of this part of the brain. It is here that the incoming signal from the optic nerves of the two eyes is processed in parallel by several billion neurons (there are only a million fibers in each optic nerve) (Fig. 2a). Figure 2b illustrates a slice through a small section of cortical tissue in V1 showing the functional structure. This is a synthesis from hundreds of experiments (Livingstone and Hubel 1988) revealing regions that process the signal in three distinct ways; some areas break down the incoming information into local color difference information, other areas contain neurons that respond preferentially to moving patterns, and a third type of area breaks down the information into local orientation and size information providing the elements of both form perception and texture perception. The regions provide different visual channels that separate different kinds of visual information. It is important to emphasize the parallel nature of this processing, whereby every part of the image falling on the retina is simultaneously decomposed through these mechanisms; the image is broken down in terms of color differences, moving elements, and the basic form and shape perception (local orientation and size).
There is general consensus that the orientation detectors in V1 form part of a contour detection mechanism that is critical for detecting the boundaries of objects. Neurons that are smoothly aligned tend to mutually reinforce one another, whereas those that are not aligned are mutually inhibitory (Field et al. 1993). The result is a kind of winner-take-all effect for aligned contour segments: they stand out clearly whereas nonaligned segments are deemphasized. This mechanism both reinforces the perception of smoothly varying continuous contours and sharpens up orientation tuning as illustrated in Fig. 2c.
Central to our theory is the following principle: to show flow orientation clearly, a display should be designed so that, as far as possible, all neurons that encode orientation should signal orientations that are tangential to the flow direction. Responses that are not tangential to the flow direction will lead to incorrect judgments of flow orientation (Ware 2008). If we consider the use of short line segments to represent a vector field, then this theory predicts that certain arrangements of the lines will be more effective than others. Many visualizations of flow use a simple grid of arrows or wind barbs to show the vector field (e.g., Trafton and Hoffman 2007). Figure 3a suggests that this will not be as effective in stimulating tangential responses as other solutions. Also, an arrow grid will cause a neural response to the grid itself, an irrelevant distraction. Arranging arrows so that they are smoothly aligned (Fig. 3b) will be better, but best of all will be a visualization consisting of continuous streamlines (Fig. 3c). This theoretical proposition has been supported both by experiments with humans and by models that computationally simulate the processing of contours in the human visual cortex (Pineo and Ware 2010).
SHOWING THE VECTOR SIGN.
It is common to decompose vectors into components of direction and magnitude (speed in the case of flow pattern). When discussing the visualization of vector fields it is useful to further decompose direction into orientation and sign as shown in Fig. 4.
A continuous contour, such as a streamline, tangential to flow direction may provide the best way of showing flow orientation but it is still ambiguous with respect to direction. To resolve the directional ambiguity some form of asymmetry along the contour is needed. Arrowheads are a common way of providing along-contour asymmetry, but they are likely not the best way. A neural mechanism that can encode directionality is a type of V1 neuron called an end stopped cell, and such cells respond best to lines that terminate in the receptive field of the cell from a particular direction. While a conventional arrow will provide some asymmetry of response, because the head will provoke a stronger response than the tail, a stronger asymmetrical response will come from other patterns. Examples are given in Fig. 5b. Such glyphs are not new; Tufte (1983) reproduces a map of North Atlantic currents drawn by Sir Edmund Halley in 1686, using elongated teardrop streamlets arranged head to tail in streamlines. However, use of these types of glyphs is almost unknown in modern practice.
STREAMLETS TO SHOW OCEAN CURRENT PATTERNS.
The theory we have outlined suggests that in order to show a vector field map, the best solution will be to use a dense pattern of streamlines and along each streamline place elements that have a much stronger head than tail. To put this theory into practice, we implemented Jobard and Lefer's (1997) algorithm to create equally spaced streamlines. Along the streamlines are placed streamlets, graphical elements that have a much more salient head than tail.
We carried out a human-in-the-loop optimization study to determine values for the remaining free parameters, such as how to represent flow speed, how to space the streamlines, the head and tail size, and the head and tail transparency of the streamlets (Mitchell et al. 2009). Our interface had a set of interactive sliders enabling study participants to adjust each of the 22 parameters controlling the mapping of the data to a display, starting from random values. Participants were instructed to produce the best representation they could. Some participants were designers and others meteorologists. A portrayal method based on the best results from the study were integrated into our FlowVis2D software, a package written in C++ and OpenGL for rendering currents from ocean model output or winds from weather model output. The result is shown in Fig. 6, in this instance illustrating surface water currents from the U.S. Navy Operational Coastal Ocean Model (NCOM). It is also used to portray forecast guidance from the NOAA/National Ocean Service's (NOS) estuarine and Great Lakes oceanographic forecast modeling systems and has been available on NOS' nowCOAST portal (http://nowcoast.noaa.gov) since 2009.
MULTIVARIATE METEOROLOGICAL DISPLAY.
In meteorological displays, a major challenge is to simultaneously show scalar variables, such as atmospheric pressure and surface air temperatures, together with wind patterns. To meet this challenge, we took advantage of the perceptual channel theory outlined in our introduction. The key design idea is to use different visual channels to show different types of information and thereby reduce visual interference between the layers. We began with the following mappings:
Temperature → color channel
Atmospheric pressure → texture channel
Wind speed and direction → motion channel
Wind patterns are represented using a pattern of 10,000 animated streamlets. To represent pressure, we used a series of graduated textures in addition to contours. To represent surface air temperatures we used a fairly conventional color sequence with different color bands every 5 degrees. The result is shown in Fig. 7 (without animation). In our evaluation, we measured a subject's ability to accurately judge temperature, pressure, and wind speed and direction, comparing our new solution with a more conventional alternative (Fig. 8a), a glyph-based alternative (Fig. 8b), and a nonanimated version of Fig. 7 (Ware and Plumlee 2012). The results showed our animated design to be perceptually more accurate than the others in the representation of wind direction and speed. It was also judged to be greatly superior in terms of how well specific wind patterns could be seen, such as weather fronts and the circulation around a low pressure center.
A BETTER WIND BARB.
A common graphical device for showing wind speed and direction is the wind barb. Wind barbs were originally designed to represent wind speed and direction at observing platforms on a surface weather map in a way that can be directly read by someone familiar with station model symbology. However, winds barbs are not well designed to show patterns of winds such as those produced by meteorological models or analysis systems. The perceptual problem with wind barbs is that only the very tip of the barb is tangential to the wind direction, and therefore most of the contours in the glyph are oriented in nontangential directions. We undertook a study to both design and evaluate alternatives to the classic wind barb with the goal of combining the best feature of the wind barb, displaying speed in a readable form, with the best feature of streamlines, showing wind patterns clearly. Two of our most successful designs are shown in Fig. 9. Our first solution used the Jobard and Lefer (1997) algorithm to generate equally spaced streamlines and placed wind barbs with curved shafts along streamlines. This improves the ability to see patterns, but the feathers of the barb still produce significant visual interference because they are not tangential to the flow direction. In a more radical redesign (Fig. 9c), arrowheads of different sizes and styles are used to replace the barb bars, showing 5-, 10-, and 50-kt increments (1 kt = 0.51 m s−1). This has the advantage of symmetry about the streamlines producing less systemic visual bias to the flow direction. It also allows for streamlines to be placed somewhat closer together, allowing for more details to be shown. Our evaluation showed the new designs to be superior in their ability to accurately show the wind speed and direction (Pilar and Ware 2013). We also evaluated the new designs in their ability to represent wind patterns. To do this, we artificially created six different wind patterns (two are shown in Fig. 10) embedded in a larger-scale smooth flow. Study participants were required to guess which of the six they were seeing under various display conditions, including the four that are illustrated. The results showed errors reduced by about 70% in comparison with the grid of wind barbs.
REPRESENTING WAVE PATTERNS.
Our final example is an extension of the alternative wind barb design. As illustrated in Fig. 11, we developed a quantitative glyph to show wave height and the direction of travel as forecast by a NWS wave model. This encodes information in a manner similar to a wind barb using symbolic bars and triangles. Wind information is also shown using our redesign of wind barbs. Two perceptual methods are used to minimize the visual interference between wave information and wind information. Because mariners are often interested in the angle of wave fronts, as opposed to the direction of travel, we draw contours that are tangential to wave fronts, and orthogonal to direction of travel. This tends to minimize visual interference between wind and wave patterns because, most of the time, wave fronts are roughly orthogonal to wind direction. Also, perceptual research shows that graphical elements that are counterphase to the background in terms of lightness can be easily separated (Theeuwes and Kooi 1994), so we use black for the wave information and white for the wind information.
CONCLUSIONS AND RECOMMENDATIONS.
Our experience suggests that an understanding of basic perceptual processes can help in the design of clear and effective visualization of meteorological and oceanographic analyses and forecast model guidance. But perceptual theory can only motivate promising approaches; it cannot be used to specify detailed design solutions. A kind of cognitive task analysis is required for a successful design. This involves determining the goals of the visual data representation. What patterns are likely to be most important for the user? Visualizations are always tradeoffs. If only wind patterns were important, then a much denser mesh of animated particle traces could have been used in Fig. 7. If it were only necessary to see atmospheric pressure and not temperature too, then color might have been used to represent pressure. The relative salience of different features must be carefully tuned in the design process to meet the design goals.
Ideally evaluation will also be part of the design process. Both formal and informal experiments with human participants are useful both to set parameter values for the mapping from data to display and to compare a new design against existing alternatives. For most of our studies we took the most basic tasks to be judgments of wind orientation, direction, or speed. Additional research is needed to discover the optimal way of bringing out patterns such as wind shear at a front, or the branching of the jet stream. However, so long as tasks can be understood and defined, perceptual theory can be applied to the problem.
One of the more difficult problems in designing effective wind, current, or wave visualizations is dealing with the scale of the map. A great advantage of color coding values such as wind speed or surface temperature is that color tends to scale well. This is because with a well-chosen color scheme, even if certain details cannot be seen, their colors will blend in the visual receptors to something approximating an average. This is not the case for vector representations, whether conventional arrows are used or one of the methods advocated here. There is an optimal element spacing for showing the greatest amount of detail; if the spacing is too small, patterns will become invisible, if too large, detail will be lost. The representation must therefore change with scale.
The development, maintenance, and operation of weather and oceanographic forecast modeling systems and their underlying numerical three-dimensional models is a hugely expensive undertaking but the cost is justified by the high value of the data. Some of the resulting products are only viewed by specialists, whereas others are seen by millions who have a more casual interest. In either case the visual portrayal of the output of these models deserves substantial effort because this is usually the only way model results can be interpreted. With a poor visualization, much of the information may be lost and a proportionate amount of modeling effort and operational costs wasted. Designing and evaluating representations for perceptual efficiency is not a trivial undertaking, but it is worth the effort.
Funding for this project was provided by NOAA Grant NA05NOS4001153 and by NSF ITR Grant 0324899. The authors thank Jason Greenlaw, Matthew Plumlee, and Roland Arsenault for their help in improving FlowVis2D software in NOS' nowCOAST GIS-based web mapping portal. We also thank Matthew Plumlee, Peter Mitchell, and Daniel Pineo, who participated in the research.